The Smithsonian has undertaken to portray in a single new hall the development of Western Civilization from the last Ice Age to the fall of Rome. The Institution has not succeeded totally but neither has it failed, which is as much as can be said for what we are pleased to call Western Civilization.

The hall, which opens Friday in the Museum of Natural History at 10th and Constitution NW, offers such a richness of artifacts that viewers probably should not try to swallow it all in one pass. It will be there for a couple of decades, so there's plenty of time to savor the 2,000 objects.

"What we have tried to present is a sense of the changing relationship of man to his environment and of people to each other," said Robert Evans, who with co-consultant Brian Hesse has spent the past three years planning the hall and choosing the exhibits. Examples of common objects, both ordinary and grand, in use over a span of 30,000 years, are designed to demonstrate the continuity of human culture.

If Evans and Hesse had had their druthers, there would be fewer than half as many items shown, but their original conception was rejected. The hall goes sharply against the current museum fashion of presenting only the best examples of a given type to avoid diluting the impact on the observer.

"The thing we're afraid of is that this will be just too much, too overwhelming," Hesse said. He's right, but that doesn't make the decision wrong. There is a strong tendency among modern practitioners of "museum science" to underestimate the public, and to present simple little displays for our simple little minds.

Anyone who wants to flit through the hall can hit the high spots in half an hour; others will find themselves spending that much time considering, say, a single case of spearpoints that show the care of a loving artist no less than of a hungry hunter.

Among the riches are some of the finest examples recovered by the monomaniacal Heinrich Schliemann, who searched through Greece with his Homer in his hand until he unearthed the supposedly legendary city of Troy. Most of what he found vanished in the German holocaust, and the rest has been out of sight in the Smithsonian's attic for a quarter of a century.

The exhibit opens with photographs of drawings from cave walls (which might work better if the display were large enough to give a sense of being inside a cavern) and reminds us right off that the cave-dwellers were every bit our intellectual and aesthetic equals. Progressing through camp to village to town to city, nation-state and empire, the visitor is surprised to learn that as people grew more urban they dwindled in size (although the mummy of a not-unifromly small Egyptian quarry superintendent will give many a man pause).

"Some of our calculations on average height and weight are conjectural, because of a limited number of measurements to work from," Hesse said, "but there is no question that the vigorous life and highmeat diet of the hunter made him bigger than even most modern men. The switch to grain as the major source of protein made him progressively smaller."

One gets the impression that while increasing urbanization made us more timid, it also made us more tender; two Bronze Age burial caves, excavated by Donald Ortner beside the Dead Sea and painstakingly reconstructed, show an increasing respect for the dead, for whose use in the afterlife especially fine pottery was developed. And the mummy of a sacred Egyptian cat is almost too affecting.

Inspired homely touches relieve the mind-weariness from time to time: A clay-tablet tally of domestic animals, probably made by a tax collector, is added up wrong; recipes and kitchen pots show that Romans then and Romans now cooked pretty much the same things in much the same way.